d-orthogonality via generating functions

Authors:
Y. Ben Cheikh;A. Zaghouani
Affiliations:
Département de mathématiques, Faculté des sciences, Tunisia;Institut préparatoire aux études d'ingénieur de Bizerte., Université de Carthage, Jarzouna Bizerte, Tunisia
Venue:
Journal of Computational and Applied Mathematics - Special issue: Special functions in harmonic analysis and applications
Year:
2007

Citing 12
Cited 2

Vector orthogonal relations. Vector QD-algorithm

Journal of Computational and Applied Mathematics - Extrapolation and Padé approximation
A characterization of “classical” d-orthogonal polynomials

Journal of Approximation Theory
The relation of the d-orthogonal polynomials to the Appell polynomials

Journal of Computational and Applied Mathematics
On a system of “classical” polynomials of simultaneous orthogonality

Journal of Computational and Applied Mathematics
On d-orthogonal Tchebychev polynomials, I

Applied Numerical Mathematics
Semiclassical multiple orthrogonal polynomials and the properties of Jacobi-Bessel polynomials

Journal of Approximation Theory
Multiple orthogonal polynomials

Journal of Computational and Applied Mathematics
Some classical multiple orthogonal polynomials

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Some discrete multiple orthogonal polynomials

Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Orthogonality of some polynomial sets via quasi-monomiality

Applied Mathematics and Computation
Some results on quasi-monomiality

Applied Mathematics and Computation - Special issue: Advanced special functions and related topics in differential equations, third Melfi workshop, proceedings of the Melfi school on advanced topics in mathematics and physics
Some discrete d-orthogonal polynomial sets

Journal of Computational and Applied Mathematics

On Askey-scheme and d-orthogonality, I: A characterization theorem

Journal of Computational and Applied Mathematics
Full length article: d-orthogonality of discrete q-Hermite type polynomials

Journal of Approximation Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, starting from a suitable generating function of a polynomial set, we show how to decide whether the considered polynomial set is d-orthogonal and, if it is so, how to determine the corresponding d-dimensional functional vector. Then, we apply the obtained results to some known and new d-orthogonal polynomial sets. For the known ones, we give new proofs for some already obtained results.